Chapter 20 Swaps

[thanhtam92]

Hi @David Harper CFA FRM, can you explain to me how you get the CFs of 0.5 in the screenshot below? Also, you introduced many to value a swap in this chapter, are both methods will be tested on the exam?

 

[Sixcarbs]

Hi @David Harper CFA FRM, can you explain to me how you get the CFs of 0.5 in the screenshot below? Also, you introduced many to value a swap in this chapter, are both methods will be tested on the exam?

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This is one of my weakest subjects, so that's why I want to try and answer this.

The Forward Libor rates, and the 2-year swap rates are all semi annual but quoted for the year. In other words, 5% semi-annual would pay 2.5% of the principal twice a year.

So for each period you need to multiply by .5 (Divide by 2) to get the payment for that period.

You can see each cash flow is the difference between the Forward rate and the swap rate, divide by 2, and discounted to the present using the spot rate.

I hope this helps.

 

[David Harper CFA FRM]

Thank you @Sixcarbs ! And @thanhtam92 I would add the following. Hull's setup question is copied below. As I often say, we want to assume all inputs in per annum term and we want to express outputs in per annum terms. Probably the most common discrete frequency (aka, periodicity) is semi-annual like this question. It's a hard question because the OIS zero rates are given with continuous compounding, but the six-month LIBOR rates are given with semi-annual compounding. But this is necessary because cash flows don't get paid continuously, cash flows get paid discretely; in this case, every six months. So the forward LIBOR(1.5, 2.0) sort of really needs to be discrete, or it's a mismatch. Hull always assumes continuous rates for the spot/zero because it's super convenient, but spot rates are easily continuous because they just discount from a point in time; e.g., S(1.5). In this example, it's almost necessary (or at least it is natural) to use a semi-annual (discrete) rate on the LIBOR because the swap rate is paying cash flows every six months. Then to Sixcarbs point, the 0.5 multiplier is acting on the 5.0% per annum swap rate because, as an input, it should be the annualized rate. So, it's very typical in bond/swap calculations to be multiplying by 0.5 when the cash flows (coupons) pay semi-annually. (Unless the problem specifically sets up an annual cash flow situation. GARP has definitely done both annual and semi-annual, GARP like annual periodicity problems, too). RE: "are both methods will be tested on the exam?" Um, do you mean valuation of swap per "as two bonds," versus "as sequence of FRA?" The approach (method) should not generally matter. GARP has asked swap problems where two approaches could be used such that you could use either. I do not think the exam will care about which approach is used, I think these problems tend to look for the numerical answer. BTW, I just quickly scanned GARP's 2020 P1 practice exam and it appears to me their swap-type questions assume semi-annual periods. I hope that's helpful,

Hull's example upon which the above is based:

Example 7.2 Suppose that the 6-month, 12-month, 18-month, and 24-month OIS zero rates (with continuous compounding) are 3.8%, 4.3%, 4.6%, and 4.75%, respectively. Suppose further that the six-month LIBOR rate is 4% with with semiannual compounding. The forward LIBOR rate for the period between 6 and 12 months is 5% with semiannual compounding. The forward LIBOR rate for the period between 12 and 18 months is 5.5% with semiannual compounding. We show how the forward LIBOR rate for the 18- to 24-month period can be calculated." -- Hull, John C.. Options, Futures, and Other Derivatives (Page 167). Pearson Education. Kindle Edition.

 

[thanhtam92]

@David Harper CFA FRM nad @Sixcarbs , thanks a lot for the reponses.